{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Beta分布\n",
    "***\n",
    "## Definition\n",
    "beta分布可以看作一个概率的概率分布，当你不知道一个东西的具体概率是多少时，它可以给出了所有概率出现的可能性大小\n",
    "\n",
    "举一个简单的例子，熟悉棒球运动的都知道有一个指标就是棒球击球率(batting average)，就是用一个运动员击中的球数除以击球的总数，我们一般认为0.266是正常水平的击球率，而如果击球率高达0.3就被认为是非常优秀的。现在有一个棒球运动员，我们希望能够预测他在这一赛季中的棒球击球率是多少。你可能就会直接计算棒球击球率，用击中的数除以击球数，但是如果这个棒球运动员只打了一次，而且还命中了，那么他就击球率就是100%了，这显然是不合理的，因为根据棒球的历史信息，我们知道这个击球率应该是0.215到0.36之间才对啊。对于这个问题一个最好的方法就是用beta分布，这表示在我们没有看到这个运动员打球之前，我们就有了一个大概的范围。beta分布的定义域是(0,1)这就跟概率的范围是一样的。接下来我们将这些先验信息转换为beta分布的参数，我们知道一个击球率应该是平均0.27左右，而他的范围是0.21到0.35，那么根据这个信息，我们可以取α=81,β=219（击中了81次，未击中219次）\n",
    "\n",
    "之所以取这两个参数是因为：\n",
    "- beta分布的均值是从图中可以看到这个分布主要落在了(0.2,0.35)间，这是从经验中得出的合理的范围。\n",
    "- 在这个例子里，我们的x轴就表示各个击球率的取值，x对应的y值就是这个击球率所对应的概率。也就是说beta分布可以看作一个概率的概率分布。\n",
    "\n",
    "<img src=\"5.png\" style=\"width:450px;height:480px;float:left\">\n",
    "\n",
    "<img src=\"6.png\" style=\"width:450px;height:480px;float:left\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(15,8))\n",
    "datas = np.linspace(0, 1, 200)\n",
    "plt.fill_between(datas,stats.beta.pdf(datas, a=5, b=10),hatch=\"+\")\n",
    "plt.fill_between(datas,stats.beta.pdf(datas, a=100, b=20),hatch=\"//\")\n",
    "plt.fill_between(datas,stats.beta.pdf(datas, a=20, b=60),hatch=\"*\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
